WOLFRAM SYSTEM MODELER

# kc_approxForcedConvection # Wolfram Language

In:= `SystemModel["Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.General.kc_approxForcedConvection"]`
Out:= # Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

Approximate calculation of the mean convective heat transfer coefficient kc for forced convection with a fully developed fluid flow in a turbulent regime.

#### Functions kc_approxForcedConvection and kc_approxForcedConvection_KC

There are basically three differences:

• The function kc_approxForcedConvection is using kc_approxForcedConvection_KC but offers additional output variables like e.g. Reynolds number or Nusselt number and failure status (an output of 1 means that the function is not valid for the inputs).
• Generally the function kc_approxForcedConvection_KC is numerically best used for the calculation of the mean convective heat transfer coefficient kc at known mass flow rate.
• You can perform an inverse calculation from kc_approxForcedConvection_KC, where an unknown mass flow rate is calculated out of a given mean convective heat transfer coefficient kc

#### Restriction

• Constant wall temperature or constant heat flux
• Turbulent regime (Reynolds number 2500 < Re < 1e6)
• Prandtl number 0.5 ≤ Pr ≤ 500

#### Calculation

The mean convective heat transfer coefficient kc is approximated through different Nusselt number Nu correlations out of [Bejan 2003, p. 424 ff].
Roughest approximation according to Dittus/Boelter (1930):

```    Nu_1 = 0.023 * Re^(4/5) * Pr^(exp_Pr)
```

Middle approximation according to Sieder/Tate (1936) considering the temperature dependence of the fluid properties:

```    Nu_2 = 0.023 * Re^(4/5) * Pr^(1/3) * (eta/eta_wall)^(0.14)
```

Finest approximation according to Gnielinski (1976):

```    Nu_3 = 0.0214 * [Re^(0.8) - 100] * Pr^(0.4) for Pr ≤ 1.5
= 0.012 * [Re^(0.87) - 280] * Pr^(0.4) for Pr > 1.5
```

The mean convective heat transfer coefficient kc is calculated by:

```    kc =  Nu * lambda / d_hyd
```

with

 eta as dynamic viscosity of fluid [Pa.s], eta_wall as dynamic viscosity of fluid at wall temperature [Pa.s], exp_Pr as exponent for Prandtl number w.r.t. Dittus/Boelter (0.4 for heating or 0.3 for cooling) [-], kc as mean convective heat transfer coefficient [W/(m2.K)], lambda as heat conductivity of fluid [W/(m.K)], d_hyd as hydraulic diameter [m], Nu_1/2/3 as mean Nusselt number [-], Pr as Prandtl number [-], Re as Reynolds number [-].

#### Verification

The mean Nusselt number Nu representing the mean convective heat transfer coefficient kc for Prandtl numbers of different fluids is shown in the figure below.

Dittus/Boelter (target = Modelica.Fluid.Dissipation.Utilities.Types.kc_general.Rough) Sieder/Tate (Target = Modelica.Fluid.Dissipation.Utilities.Types.kc_general.Middle) Gnielinski (Target = Modelica.Fluid.Dissipation.Utilities.Types.kc_general.Finest) Note that all fluid properties shall be calculated with the mean temperature of the fluid between the entrance and the outlet of the generic device.

#### References

Bejan,A.:
Heat transfer handbook. Wiley, 2003.